Problem: $B$ is the midpoint of $\overline{AC}$ $A$ $B$ $C$ If: $ AB = 4x + 3$ and $ BC = 7x - 24$ Find $AC$.
Solution: A midpoint divides a segment into two segments with equal lengths. ${AB} = {BC}$ Substitute in the expressions that were given for each length: $ {4x + 3} = {7x - 24}$ Solve for $x$ $ -3x = -27$ $ x = 9$ Substitute $9$ for $x$ in the expressions that were given for $AB$ and $BC$ $ AB = 4({9}) + 3$ $ BC = 7({9}) - 24$ $ AB = 36 + 3$ $ BC = 63 - 24$ $ AB = 39$ $ BC = 39$ To find the length $AC$ , add the lengths ${AB}$ and ${BC}$ $ AC = {AB} + {BC}$ $ AC = {39} + {39}$ $ AC = 78$